Sure, but I guess an ICE/ICD (In-Circuit-Emulator/Debugger) for a modern CPU will cost a couple of hundred thousand dollars.
For a modern processor, "ICE" means something different than what you are thinking of. NO one debugs with a true "ICE" any more,
Not "no one" -- but for the purposes we're talking about here, it's pretty close yes.
Adding to Ron's homebrew stuff:
http://www.mouser.com/search/refine.aspx?Ntt=DLP-2232M-G
is a $35 board that very easily talks JTAG from USB.
Ooh, nice! And a bunch of CPIOs and a 232 port at the same time, too. With drivers and example code and everything.
Do note that for debugging a "modern" processor you still need to know what JTAG commands to send (and many manufacturers don't publicly document this).
Segher